The cyclic integral of actual heat exchange over temperature is non-positive, whereas entropy change is defined strictly through reversible heat. What does this distinction mean for evaluating system transformations?

B. Actual transferred heat is only a lower bound on the true change in entropy

Because the Clausius inequality bounds the cyclic integral below zero, the real irreversible heat transferred along a path yields less than the genuine state difference ΔS. Entropy is never destroyed, nor does a state function retain any memory of past heat paths.